Hydraulic Capacity Formula:
Q = A × V
Where:
- Q = Flow capacity (m³/s or ft³/s)
- A = Cross-sectional area of pipe (m² or ft²)
- V = Flow velocity (m/s or ft/s)
Manning’s Equation for Velocity (V):
V = (1.486/n) × R^(2/3) × S^(1/2) (imperial units)
or
V = (1/n) × R^(2/3) × S^(1/2) (metric units)
Where:
- n = Manning’s roughness coefficient (0.022-0.027 for corrugated metal)
- R = Hydraulic radius (A/P, where P is wetted perimeter)
- S = Slope of energy grade line (pipe slope for uniform flow)
Example Calculation:
For a 48-inch diameter corrugated metal arch pipe (n=0.024) at 0.5% slope flowing half-full:
- A = π×(4ft)²/8 = 6.28 ft²
- P = π×4ft/2 = 6.28 ft
- R = A/P = 1 ft
- V = (1.486/0.024) × 1^(2/3) × 0.005^(1/2) ≈ 4.4 ft/s
- Q = 6.28 × 4.4 ≈ 27.6 cfs (ft³/s)
Note: Actual design should consider tailwater conditions, entrance losses, and other hydraulic factors.